Is there a visual modeling language or style for the functional programming paradigm?

Question

UML is a standard aimed at the modeling of software which will be written in OO languages, and goes hand in hand with Java. Still, could it possibly be used to model software meant to be written in the functional programming paradigm? Which diagrams would be rendered useful given the embedded visual elements?

Is there a modeling language aimed at functional programming, more specifically Haskell? What tools for putting together diagrams would you recommend?

Edited by OP Sept 02, 2009:

What I'm looking for is the most visual, lightest representation of what goes on in the code. Easy to follow diagrams, visual models not necessarily aimed at other programmers. I'll be developing a game in Haskell very soon but because this project is for my graduation conclusion work I need to introduce some sort of formalization of the proposed solution. I was wondering if there is an equivalent to the UML+Java standard, but for Haskell. Should I just stick to storyboards, written descriptions, non-formalized diagrams (some shallow flow-chart-like images), non-formalized use case descriptions?

Edited by jcolebrand June 21, 2012:

Note that the asker originally wanted a visual metphor, and now that we've had three years, we're looking for more/better tools. None of the original answers really addressed the concept of "visual metaphor design tool" so ... that's what the new bounty is looking to provide for.

Answer 1

I believe the modeling language for Haskell is called " math ". It's often taught in schools.

Answer 2

Yes, there are widely used modeling/specification languages/techniques for Haskell. They're not visual.

In Haskell, types give a partial specification. Sometimes, this specification fully determines the meaning/outcome while leaving various implementation choices. Going beyond Haskell to languages with dependent types, as in Agda & Coq (among others), types are much more often useful as a complete specification.

Where types aren't enough, add formal specifications, which often take a simple functional form. (Hence, I believe, the answers that the modeling language of choice for Haskell is Haskell itself or "math".) In such a form, you give a functional definition that is optimized for clarity and simplicity and not all for efficiency. The definition might even involve uncomputable operations such as function equality over infinite domains. Then, step by step, you transform the specification into the form of an efficiently computable functional program. Every step preserves the semantics (denotation), and so the final form ("implementation") is guaranteed to be semantically equivalent to the original form ("specification"). You'll see this process referred to by various names, including "program transformation", "program derivation", and "program calculation".

The steps in a typical derivation are mostly applications of "equational reasoning", augmented with a few applications of mathematical induction (and co-induction). Being able to perform such simple and useful reasoning was a primary motivation for functional programming languages in the first place, and they owe their validity to the "denotative" nature of "genuinely functional programming". (The terms "denotative" and "genuinely functional" are from Peter Landin's seminal paper The Next 700 Programming languages .) Thus the rallying cry for pure functional programming used to be "good for equational reasoning", though I don't hear that description nearly as often these days. In Haskell, denotative corresponds to types other than IO and types that rely on IO (such as STM ). While the denotative/non- IO types are good for correct equational reasoning, the IO /non-denotative types are designed to be bad for incorrect equational reasoning.

A specific version of derivation-from-specification that I use as often as possible in my Haskell work is what I call "semantic type class morphisms" (TCMs). The idea there is to give a semantics/interpretation for a data type, and then use the TCM principle to determine (often uniquely) the meaning of most or all of the type's functionality via type class instances. For instance, I say that the meaning of an Image type is as a function from 2D space. The TCM principle then tells me the meaning of the Monoid , Functor , Applicative , Monad , Contrafunctor , and Comonad instances, as corresponding to those instances for functions. That's a lot of useful functionality on images with very succinct and compelling specifications! (The specification is the semantic function plus a list of standard type classes for which the semantic TCM principle must hold.) And yet I have tremendous freedom of how to represent images, and the semantic TCM principle eliminates abstraction leaks. If you're curious to see some examples of this principle in action, check out the paper Denotational design with type class morphisms .

Answer 3

We use theorem provers to do formal modelling (with verification), such as Isabelle or Coq. Sometimes we use domain specific languages (eg Cryptol) to do the high level design, before deriving the "low level" Haskell implementation.

Often we just use Haskell as the modelling language, and derive the actual implementation via rewriting.

QuickCheck properties also play a part in the design document, along with type and module decompositions.

Answer 4

Yes, Haskell.

I get the impression that programmers using functional languages don't feel the need to simplify their language of choice away when thinking about their design, which is one (rather glib) way of viewing what UML does for you.

Answer 5

I have watched a few video interviews, and read some interviews, with the likes of erik meijer and simon peyton-jones. It seems as when it comes to modelling and understanding ones problem domain, they use type signatures, especially function signatures.

Sequence diagrams (UML) could be related to the composition of functions. A static class diagram (UML) could be related to type signatures.

Answer 6

In Haskell, you model by types.

Just begin with writing your function-, class- and data signatures without any implementation and try to make the types fit. Next step is QuickCheck.

Eg to model a sort:

class Ord a where
    compare :: a -> a -> Ordering

sort :: Ord a => [a] -> [a]
sort = undefined

then tests

prop_preservesLength l = (length l) == (length $ sort l)
...

and finally the implementation ...

Answer 7

Although not a recommendation to use (as it appears to be not available for download), but the HOPS system visualizes term graphs, which are often a convenient representation of functional programs.

It may be also considered a design tool as it supports documenting the programs as well as constructing them; I believe it can also step through the rewriting of the terms if you want it to so you can see them unfold .

Unfortunately, I believe it is no longer actively developed though.

Answer 8

I realize I'm late to the party, but I'll still give my answer in case someone would find it useful.

I think I'd go for systemic methodologies of the likes of SADT/IDEF0.

• https://en.wikipedia.org/wiki/Function_model
• https://en.wikipedia.org/wiki/Structured_Analysis_and_Design_Technique

Such diagrams can be made with the Dia program that is available on both Linux, Windows and MacOS.

Answer 9

You can a data flow process network model as described in Realtime Signal Processing: Dataflow, Visual, and Functional Programming by Hideki John Reekie

For example for code like (Haskell):

fact n | n == 0    = 1
       | otherwise = n * fact (n - 1)

The visual representation would be:

Answer 10

What would be the point in modelling Haskell with Maths? I thought the whole point of Haskell was that it related so closely to Maths that Mathematicians could pick it up and run with it. Why would you translate a language into itself?

When working with another functional programming language (f#) I used diagrams on a white board describing the large blocks and then modelled the system in an OO way using UML, using classes. There was a slight miss match in the building blocks in f# (split the classes up into data structures and functions that acted upon them). But for the understanding from a business perspective it worked a treat. I would add mind that the problem was business/Web oriented and don't know how well the technique would work for something a bit more financial. I think I would probably capture the functions as objects without state and they should fit in nicely.

It all depends on the domain your working in.

Answer 11

I use USL - Universal Systems Language. I'm learning Erlang and I think it's a perfect fit.

Too bad the documentation is very limited and nobody uses it. More information here .